Problem: Simplify the following expression: $\sqrt{63} - \sqrt{7}$
Answer: First, try to factor any perfect squares out of the radicals. $= \sqrt{63} - \sqrt{7}$ $= \sqrt{9 \cdot 7} - \sqrt{7}$ Separate the radicals and simplify. $= \sqrt{9} \cdot \sqrt{7} - \sqrt{7}$ $= 3\sqrt{7} - \sqrt{7}$ Finally, simplify by combining the terms. $= ( 3 - 1 )\sqrt{7} = 2\sqrt{7}$